The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies

In this paper, under the assumption of Hölder continuous coefficients, we prove the strong Feller property for the solution to a one-dimensional Lévy processes driven stochastic differential equations. Our proof are based on the tools of Yamada-Watanabe approximation technique, Girsanov’s theorem and coupling method. Using this approach, the continuous dependence on initial data for the same equations

This paper presents an iterative formulation to compute the central moments of the matrix Fisher distribution on the three dimensional special orthogonal group up to an arbitrary order.

The taboo rate is first defined, which satisfies with the Chapman–Kolmogorov equation. Then the differentials of hitting time distribution are expressed by many different taboo rates, which deeply reveal the intrinsic relationship between the transition rate matrix and the hitting time distribution in continuous-time reversible Markov chains. As an example, the explicit expressions of the differentials

We propose a double selection instrumental variable estimator for the endogenous treatment effects using both high-dimensional control variables and instrumental variables. It deals with the endogeneity of the treatment variable and reduces omitted variable bias due to imperfect model selection.

For linear mixed models having two variance components, one can compute exact confidence intervals for a ratio of the variances. We show that there is a family of unbiased intervals and highlight those unbiased intervals which have short expected length.

In this paper, we propose an estimator of the generalized maximum mean discrepancy between several probability distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these distributions and under the alternative hypothesis, so allowing to achieve a k-sample test for equality of distributions. A simulation study that allows

In this paper we show that for any fixed Pearson correlation coefficient strictly between −1 and 1, the distance correlation coefficient can take any value in the open unit interval (0,1).

We consider Hölder classes of density functions on Riemannian manifolds in intrinsic perspectives. We develop a theorem that links such Hölder classes on Riemannian manifolds to those on Euclidean spaces. Using the theorem, we derive lower bounds to Lp-convergence rates (1≤p≤∞) for the estimation of the underlying density on a Riemannian manifold.

In this paper, we investigate the properties of BSDEs in general filtration spaces based on the transposition solutions. We obtain a result that Jensen’s inequality holds under the g-expectation and conditional g-expectation in general filtration spaces if and only if g is independent of y and super-homogeneous in z.

This paper deals with two generalizations of the classical linear structural errors-in-variables model (SEIVM) with univariate observations. In these two models, the data may no longer come from a single linear SEIVM, due to that a change in the slope in the first model and a change in the intercept in the second model may occur after observing the first k∗ data pairs, where k∗ is assumed to be unknown

In this paper, we develop a Mean Empirical Likelihood (MeanEL) method for right censored data. This MeanEL approach is based on traditional empirical likelihood methods but uses synthetic data to construct an EL ratio statistics, which is shown to have a χ2 limiting distribution. Different simulation studies show that the MeanEL confidence intervals tend to have more accurate coverage probabilities

Using Kendall’s tau for copulas, we compare the degree of concordance of random variables with that of their order statistics. We prove a general inequality and show that this inequality is strict for every copula from the Fréchet family which is distinct from the upper Fréchet–Hoeffding bound.

Various equicontinuity properties for families of Markov operators have been - and still are - used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically

In this paper, we consider random sequences with independent entries that are not necessarily identically distributed and obtain bounds on the maximal and minimal correlation of such sequences. We also determine sufficient conditions under which the scaled maximal and minimal correlations both converge to a common nominal value.

The Haezendonck–Goovaerts (HG) risk measure has received increasing attention in recent years. In this paper, we propose a conditional version of the HG risk measure, called CoHG risk measure. This conditional risk measure can be used to describe a causality relationship between two risk variables and to qualify the systemic risk contribution of a risk in a catastrophic scenario. We list some basic

An adjusted least absolute deviation estimating function, founded on the inverse (probability of) censoring weighted approach, is proposed. Covariate-free left and right censoring is assumed. When left censoring is absent, the proposed estimating function reduces to its right-censored counterpart. Consistency and asymptotic normality of the estimator of the regression parameter are derived. Finite

The converse comparison theorems have received much attention in the theory of BSDEs and ABSDEs. But, no such theory has been given for multidimensional ABSDEs. In this paper, we mainly study a certain kind of multidimensional ABSDEs and give the converse theorems for this type of multidimensional ABSDEs.

Analysis of sufficient dimension reduction (SDR) is an important topic and has attracts our attention in decades. Several methods have been proposed based on simple settings. In applications, however, the ultrahigh-dimensional setting with p≫n and covariate measurement error usually appear in the dataset, and it is not trivial to adopt the conventional methods to handle this problem. In this paper

In this article we study the so-called cutoff phenomenon in the total variation distance when n→∞ for the family of continuous-time stochastic processes indexed by n∈N, Ztn≔maxj∈{1,…,n}Xtjt≥0,where X1,…,Xn is a sample of n ergodic Ornstein–Uhlenbeck processes driven by stable noise of index α. It is not hard to see that for each n∈N, Ztn converges in the total variation distance to a limiting distribution

In observational studies, propensity score methods are useful for estimating causal effects. We propose a new method for selecting the optimal number of strata for subclassification on the propensity score. The proposed method achieves “optimality” in terms of the MSE.

A decision-maker who is looking to minimize the expected rank of a candidate chosen out of a large pool of sequential applicants should plan to interview slightly less than 50.65% of them on average in the no-information setting.

The novelty of this research work is to establish stability results in Ulam–Hyers sense for the nonlinear fractional stochastic neutral differential equations system with the aid of weighted maximum norm and Itô’s isometry in finite dimensional stochastic settings.

We prove some analogues of the Skitovich–Darmois, Heyde characterization theorems and other theorems of mathematical statistics for Q-independent random variables with values in a Banach space.

The Frisch–Waugh–Lovell Theorem states the equivalence of the coefficients from the full and partial regressions. I further show the equivalence between various standard errors. Applying the new result to stratified experiments reveals the discrepancy between model-based and design-based standard errors.

We have considered equicorrelated observations from normal distribution for simultaneous testing problem. In this article, we have shown that FWER asymptotically is a convex function of the correlation (ρ) and hence an upper bound on the FWER of Bonferroni-α procedure is α(1−ρ). This implies that Bonferroni’s method actually controls the FWER at a much smaller level than the desired level of significance

In recent years, several mixtures of skew factor analyzers have been proposed. These models adopt various skew distributions for either the factors or the errors, but not both. This paper examines the connections between these formulations and introduces a unified model that allows for skewness in both the factors and errors.

We give necessary and sufficient conditions for the Chebyshev integral inequality to be an equality.

The equivalence of pth (p>0) moment stability between stochastic differential delay equations and their numerical methods is studied under the assumptions that the numerical methods are strongly convergent and have the bounded pth moment in the finite time.

We establish the existence and uniqueness of global (in time) positive strong solutions for a generalized population dynamics equation with environmental noise, while the global existence fails for the deterministic equation. Particularly, we prove the global existence of positive strong solutions for the following stochastic differential equation dXt=(θXtm0+kXtm)dt+εXtm+12φ(Xt)dWt,t>0,Xt>0,m>m0⩾1

For a conditional density function (CDF) in the right-censored model, the local linear (LL) estimator has superior bias properties compared with the Nadaraya–Watson (NW) one, but it may have negative values and thus give rise to unsuitable inference. In order to alleviate the possible negativity of the LL estimator, we define a reweighted NW (RNW) estimator of the CDF in the right-censored model by

In the paper, the large deviation inequalities of the LS estimator for the nonlinear regression model with martingale differences errors are established. The assumptions for the errors are (conditional) exponential integrability which weaken the bounded condition in Hu (1993). As an application, we give the large deviation inequalities of LS estimator for the simple Michaelis–Menten model.

This article investigates the asymptotic properties of weighted least squares estimators (WLSE) for a binary random coefficient autoregressive (RCA) panel model with heterogeneous variances of panel variables. It is an extension of Johansen and Lange (2013) to a panel model, which is more practical for macroeconomic time series data. We develop asymptotic properties of the WLSE in cases of finite and

This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, for reversible Markov chain, it is proved that the exponential convergence of f-ergodicity holds if and only if the spectral gap of the generator is positive. Moreover, the convergence rate is equal to the spectral gap. For irreversible case, the positivity of spectral

This paper introduces two nonparametric recursive estimators of the copula. These estimators employ a recursive estimation of the quantile achieved using a stochastic approximation algorithm. Their asymptotic properties and numerical performance are investigated in the context of i.i.d. data.

The paper studies a critical Bienaymé–Galton–Watson branching processes with immigration in varying environments. Assuming that the offspring variance is infinite and the mean number of immigrants is either finite or infinite is proved the asymptotic formulas for the probability for non extinction. The proper limiting distributions under the appropriate normalization are also proved.

In this paper we study the sojourn time on the positive half-line up to time t of a drifted Brownian motion with starting point u and subject to the condition that min0≤z≤lB(z)>v, with u>v. This process is a drifted Brownian meander up to time l and then evolves as a free Brownian motion. We also consider the sojourn time of a bridge-type process, where we add the additional condition to return to

The von Weizsäcker theorem states that every sequence of nonnegative random variables has a subsequence which is Cesàro convergent to a nonnegative random variable which might be infinite. The goal of this note is to provide a description of the set where the limit is finite. For this purpose, we use a decomposition result due to Brannath and Schachermayer.

We propose an enhanced support detection and root finding approach (ESDAR) to variable selection in sparse linear models. ESDAR is motivated from the KKT conditions for the ℓ0 penalized regression. In ESDAR, we introduce a step size to balance the primal and dual variables in determining the support of the solution. We establish a sharp oracle error bound and an oracle support recovery property for

The probability distribution of a sequence X=(X1,X2,…) of random variables is determined by its predictive distributions P(X1∈⋅) and P(Xn+1∈⋅∣X1,…,Xn), n≥1. Motivated by applications in Bayesian predictive inference, in Berti et al. (2020), a class C of sequences is introduced by specifying such predictive distributions. Each X∈C is conditionally identically distributed. The asymptotics of X∈C is investigated

We consider Weierstraß and Takagi–van der Waerden functions with critical degree of roughness. In this case, the functions have vanishing pth variation for all p>1 but are also nowhere differentiable and hence not of bounded variation either. We resolve this apparent puzzle by showing that these functions have finite, nonzero, and linear Wiener–Young Φ-variation along the sequence of b-adic partitions

A modification to the asymptotic distribution of the T2-statistic used in multivariate process monitoring is provided when the dimension of the vectors may exceed the sample size. Under certain mild condition, a unified limit distribution is obtained that is applicable for both Phase I and II charts. Further the limit holds for charts based on individual observations as well as subgroup means. The

In the paper, upper bounds for the rate of convergence in laws of large numbers for mixed Poisson random sums are constructed. As a measure of the distance between the limit and pre-limit laws, the Zolotarev ζ-metric is used. The obtained results extend the known convergence rate estimates for geometric random sums (in the famous Rényi theorem) to a considerably wider class of random indices with mixed

Let {B(ξn,rn)}n≥1 be a sequence of random balls whose centers {ξn}n≥1 is a stationary process, and {rn}n≥1 is a sequence of positive numbers decreasing to 0. Our object is the random covering set E=lim supn→∞B(ξn,rn), that is, the points covered by B(ξn,rn) infinitely often. The sizes of E are investigated from the viewpoint of measure, dimension and topology.

In this paper we study the problem of semi-classical asymptotics for the scattering length of non-negative potentials with infinite range. It was proved analytically by Tamura (1993) that the scattering length Γ(V) of a non-negative V induced by 3-dimensional Brownian motion obeys Γ(ε−2V)∼ε−2∕(ρ−2) in the semi-classical limit ε→0, if V(x) behaves like |x|−ρ,ρ>3 at infinity. We will extend this result

In this paper we extend the usual Hidden Markov Models framework, where the observed objects are univariate or multivariate data, to the case of functional data, by modeling the temporal structure of a system of multivariate curves evolving in time.

In a multinomial set-up with k possible outcomes, we develop estimation under a “middle censoring” paradigm, which is as defined in Jammalamadaka and Mangalam (2003). This problem has many special features because of the inter-dependent probabilities, which we explore here.

We show the existence and uniqueness of the solutions of reflected stochastic differential equations driven by semimartingales with regulated trajectories. The study of these SDEs will be based on a new existence and uniqueness theorem for the deterministic Skorokhod problem when the driving process has only right and left limits.

This note introduces an asymptotically normal statistic for the value function of a convex stochastic minimization program, which may have more than one minimizer. The statistic uses a recursive estimator, based on the proximal algorithm, of one of the minimizers.

When a statistical test is repeatedly applied to rows of a data matrix, correlations among data rows will give rise to correlations among corresponding test statistics. We investigate the relationship between test-statistic correlation and data-row correlation and discuss its implications.

In this paper we consider the statistical concept for continuous-time stochastic processes, which is based on Granger’s definition of causality. We, also, show that separability is directly related to causality concepts. More precisely, we provide necessary conditions, in terms of statistical causality, for the space Lp(Ω,G∞,P) to be separable. The concept of statistical causality is related to the

We prove a strong law of large numbers for simultaneously testing parameters of a large number of dependent, Lancaster bivariate random variables with infinite supports, and discuss its implications.

Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter p of the binomial distribution are presented.

Based on an aliased component-number pattern (ACNP), a general minimum lower-order confounding (GMC) criterion has been proposed to choose the optimal regular designs, which minimize the confounding among lower-order effects. This paper is ready to study the properties of GMC s-level designs in terms of complementary sets. It is proved that an sn−m design has GMC only if its complementary set is contained

We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its starting point from the boundary. We derive as a consequence that at all times the number of particles at a site is monotonically decreasing with respect to its distance

We present analytic solutions to some optimal stopping problems for the running minimum of a geometric Brownian motion with exponential positive discounting rates. The proof is based on the reduction of the original problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping

We consider asymptotic properties of the empirical process of tempered moving average with memory parameter d∈[0,1∕2) and tempering parameter λN→0, centered by the marginal distribution function of the corresponding untempered stationary process. We prove that under long memory (0

We prove an upper bound on the Wasserstein distance between normalized martingales and the standard normal random variable, which extends a result of Röllin (2018). The proof is based on a method of Bolthausen (1982).

We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned bounds. As an example we give estimates of the excess loss in fixed design linear regression in dependent observations.

Strong laws of large numbers are obtained for non-homogeneous arbitrary dependent sequences.